MAGIC004: Applications of model theory to algebra and geometry

Course details

Semester

Autumn 2013
Monday, October 7th to Saturday, December 14th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
0

Timetable

Mondays
11:05 - 11:55

Description

This will be a 10 hour "version" of what was previously given (Spring 2008, Spring 2010) as a 20 hour course. However, I plan to be somewhat more ambitious, at the expense of leaving many details of the introductory material to be done in exercises. Among the new aspects of the new version will be the inclusion of stability theory. The first 5 hours will introduce model theory and stability theory, including stable groups. The last 5 hours will concern connections and applications, largely where groups of one form or the other are involved, and will be taken from among: geometric group theory, diophantine geometry over number fields and function fields (Manin-Mumford, Mordell-Lang), approximate subgroups,..

Prerequisites

Some familiarity with first order logic would be helpful but not essential.

Syllabus

beginitemize item textbfLectures 1 to 5: BASICS OF MODEL THEORY AND STABILITY THEORY: First order languages, structures and theories, compactness, types, saturation and homogeneity, stability, stable groups.
item textbfLecture 7 to 10: APPLICATIONS: I will cover 4 or 5 topics, explaining why and how material from the earlier lectures can give insights in areas of algebra, geometry, and number theory. More details will be given closer to the start date.
enditemize

Lecturer

  • DM

    Prof Dugald MacPherson

    University
    University of Leeds

Bibliography

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Assessment

Description

The assessment for this course will be via a single take-home paper in January with 2 weeks to complete and submit online. The exam paper will be made available online from January 4 2014.
The exam paper will focus on the parts of the course covered in the first four weeks (which are also covered by the four problem sheets). This is the material in Sections 1-4 in the online file magic2013-modeltheoryhandout.pdf and explored in the assignments. The assignments themselves are not assessed.

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Files

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Lectures

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